title: Analytical solution to heat equation with magnetic resonance experimental verification for nanoshell enhanced thermal therapy.
abstract: OBJECTIVE
  The treatment efficacy of laser-induced thermal therapy is greatly enhanced by the presence gold coated nanoshells within the tissue being treated. The nanoshells are turned to exhibit a surface plasmon resonance at the frequency of the incident laser light, dramatically increasing the therapeutic efficiency of the laser treatment. Accurate modeling of the resulting temperature distributions is essential for treatment planning. Analytic solutions are desirable because they give greater insight into the physical meaning of the different terms that contribute to the problem.
  
  
  METHODS
  The heat equation is solved by application of the Green's function method and the solution is compared to experimental temperature data for gel phantoms containing different concentrations of nanoshells. The experimental temperature data was obtained by using magnetic resonance temperature imaging methods while the gel was being heated with an 810 nm laser.
  
  
  RESULTS
  Reasonable agreement was obtained between the results of the analytic calculation and the experimental data for the various concentrations of nanoshells and laser outputs tested. This agreement was consistent for both the spatial and temporal domain. On average the disagreement between analytical calculation and experiment was 0.93+/-0.84 degrees C.
  
  
  CONCLUSIONS
  We have shown that analytic solutions to the heat equation using the Green's function approach can be used to describe experimental temperature distributions due to the presents of nanoshells for various laser powers and nanoshell concentrations.
authors.affiliation: Nanospectra Biosciences, Inc. Houston, TX, USA. elliott@di.mdacc.tmc.edu
authors.forename: Andrew
authors.initials: A
authors.lastname: Elliott
authors.forename: Jon
authors.initials: J
authors.lastname: Schwartz
authors.forename: James
authors.initials: J
authors.lastname: Wang
authors.forename: Anil
authors.initials: A
authors.lastname: Shetty
authors.forename: John
authors.initials: J
authors.lastname: Hazle
authors.forename: Jason R
authors.initials: JR
authors.lastname: Stafford
mesh_terms: D000465:Algorithms; D004595:Electroplating; D006046:Gold; D006801:Humans; D053685:Laser Therapy; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D054118:Nanospheres; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D013816:Thermodynamics; D013817:Thermography
chemical_list: D006046:Gold